Atefe Razghandi - Department of Mathematics and Computer Sciences, Hakim Sabzevari University, P.O.Box ۳۹۷, Sabzevar, Iran.
Ali Akbar Arefijamaal - Department of Mathematics and Computer Sciences, Hakim Sabzevari University, P.O.Box ۳۹۷, Sabzevar, Iran.

In this paper we consider  (extended) metaplectic representation of the  semidirect product  G_{\mathbb{J}}=\mathbb{R}^{۲d}\times\mathbb{J}  where \mathbb{J} is a closed subgroup of Sp(d,\mathbb{R}), the symplectic group. We will investigate continuous representation frame on G_{\mathbb{J}}. We also discuss the existence of duals for such frames and give several characterization for them. Finally, we rewrite the dual conditions, by using the Wigner distribution and obtain more reconstruction formulas.

Representation frames, Dilation groups, Dual frames, Continuous frames